Multivariable calculus is a branch of mathematics that extends the concepts of single-variable calculus to functions of multiple variables. It involves studying how these functions behave and change, focusing on topics like partial derivatives, multiple integrals, and vector calculus. This field is essential for understanding complex systems in physics, engineering, and economics. In multivariable calculus, tools such as gradients and divergence help analyze how functions change in different directions. Applications include optimizing functions with several variables, modeling physical phenomena, and solving problems in fields like physics, computer science, and economics.